Abstract
We present a general method to bosonize systems of fermions with infinitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, by expressing the quantized conserved electric charge- and current density in terms of a bosonic antisymmetric tensor field of rank d-1, where d is the dimension of space. This enables us to make concepts and tools from gauge theory available for the purpose of analysing electronic structure of non-relativistic matter. We apply our bosonization identities and concepts from gauge theory, such as the Wegner-'t Hooft duality, to a variety of systems of condensed matter physics: Landau-Fermi liquids, Hall fluids, London superconductors, etc. Among our results are an exact formula for the plasmon gap in a metal, a simple derivation of the Anderson-Higgs mechanism in superconductors, and an analysis of the orthogonality catastrophe for static sources.